Question

sum of two numbers is 24 and difference is12.form a pair of equationwith two letters and find the numbers​

Answer 1

Question:-

sum of two numbers is 24 and difference is 12.form a pair of equation with two letters and find the numbers

Answer:-

• The numbers are 18 and 6 respectively

To find:-

• The numbers

Solution:-

• Sum = 24
• Difference = 12

Let,

• First number = x
• Second number = y

The equations will be:

• x + y = 24............(1)
• x – y = 12.............(2)

Solve equation 1,

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: x + y = 24}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: x = 24 - y}$

Put value of x in equation 2,

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: (24 - y) - y = 12}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: 24 - 2y = 12}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: - 2y = 12 - 24}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: - 2y = - 12}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: y = \frac{ - 12}{ - 2} }$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: y = 6}$

Put value of y in equation 1,

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: x + 6 = 24}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: x = 24 - 6}$

$\Large{\sf:\implies \: \: \: \: \: \: \: \: \: x = 18}$

Hence,

The numbers are 18 and 6 respectively

Answer 2

Answer:

Let the 2 numbers be x and y with x > y

⇒x+y=12→(1)

←sum of 2 numbers

⇒x-y=4→(2)

← difference of numbers

Adding the 2 equations, term by term on both sides, will eliminate y leaving an equation in x that we can solve.

⇒(1)+(2) gives

(x+x)+(−y+y)=(4+12)

⇒2x=16

divide both sides by 2

2x/2=16/2

x=8

Substitute this value into equation ( 1 ) and solve for y

8+y=12

y=12-8=4

Thus the 2 numbers are 8 and 4

Hope it helps you

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